The tropospheric delay is one of many error sources that affect the Global Navigation Satellite System (GNSS) positioning solutions. The widely used troposphere models assume a homogeneous atmosphere so that only the zenith delay needs to be determined and is mapped through an elevation-dependent mapping function. This procedure is to reduce the computational burden and keep the positioning model full-rank. However, this assumption fails for a realistic description of the troposphere, which is always asymmetrical at a certain elevation angle, especially during a weather event when the weather conditions are very complex. These imperfectly modelled tropospheric delays may influence the positioning accuracy and integer ambiguity resolution performance. In this case, this contribution aims to investigate the effects of the model errors due to the asymmetrical troposphere on GNSS estimations. The Numerical Weather Prediction (NWP) model is applied to generate the actual ray-tracing tropospheric delay in Western Europe, and the tropospheric model errors are calculated in a normal weather condition and a weather event condition by comparing the slant delay calculated from the NWP model and the mapping function. Case studies on the same GNSS station are conducted in two weather conditions: a normal troposphere condition and a weather event with heavy rainfall. The results based on the case studies show that the troposphere in the normal weather condition is nearly homogeneous that the azimuthal-dependent discrepancies of the tropospheric delay are less than 1cm at a very low elevation angle; meanwhile, the discrepancies between different azimuthal angles can reach to more than 25cm in the weather event. A single-frequency Single Point Positioning (SPP) model and a Precise Point Positioning (PPP) model that preserves the integer property of ambiguity are chosen for studying the estimation biases caused by the troposphere model errors. It turns out that almost all horizontal positioning biases of SPP and PPP are less than 1cm in the normal weather condition; however, the scales of the horizontal and 3D biases are concentrated in 1 to 10cm in the weather event for these two models. This contribution also contains the study of the actual integer ambiguity resolution success rate in the presence of the tropospheric model errors by applying the Monte Carlo simulation, and the success rates of PPP in the normal weather condition are consistent with the theoretical values calculated with the ideal troposphere which is totally symmetrical. However, the actual success rates in the weather event are extremely low at some epochs due to the tropospheric model errors, which means that wrong fixing may occur since the theoretical values cannot take into account these model errors. Note that the horizontal tropospheric gradients are not involved in the processing, which means that an optimistic performance might be expected if the gradients are considered.

The technology of integer ambiguity resolution-enabled precise-point-positioning (also referred to as PPP-AR) has been proven capable of providing comparable accuracy, efficiency, and productivity to long-baseline real-time kinematic positioning (RTK) during the last decade. Commercial PPP-AR services have been provided by different institutions and companies and have been widely used in geodetic missions. However, the usage and research of the PPP-AR mostly concentrated on nonaviation applications, e.g., vehicle navigation, surveying, and mapping, and monitoring crustal motions. Few of them focused on fixing the ambiguities during an aircraft flight. In this contribution, we implemented the PPP-AR technique for the first time in an airplane flight test to investigate how much the fixed ambiguities could contribute to airplane positioning solutions in challenging circumstances, including high velocity and severe maneuvers. We first looked into the influences of the tropospheric delay on the positioning and ambiguity solutions because the height of the airplane may dramatically change within a narrow time span, and thus, a proper constraint of this parameter was crucial for the computation of the tropospheric effects. Then, how to fix the ambiguities successfully and reliably in challenging circumstances was discussed. Finally, the airplane data was processed in 15 and 1s intervals with ambiguity float and fixed solutions under different configurations to illustrate in which condition and to what extent the fixed ambiguities can improve the airplane positioning accuracy.

The benefits of an increased number of global navigation satellite systems (GNSS) in space have been confirmed for the robustness and convergence time of standard precise point positioning (PPP) solutions, as well as improved accuracy when (most of) the ambiguities are fixed. Yet, it is still worthwhile to investigate fast and high-precision GNSS parameter estimation to meet user needs. This contribution focuses on integer ambiguity resolution-enabled Precise Point Positioning (PPP-RTK) in the use of the observations from four global navigation systems, i.e., GPS (Global Positioning System), Galileo (European Global Navigation Satellite System), BDS (Chinese BeiDou Navigation Satellite System), and GLONASS (Global’naya Navigatsionnaya Sputnikova Sistema). An undifferenced and uncombined PPP-RTK model is implemented for which the satellite clock and phase bias corrections are computed from the data processing of a group of stations in a network and then provided to users to help them achieve integer ambiguity resolution on a single receiver by calibrating the satellite phase biases. The dataset is recorded in a local area of the GNSS network of the Netherlands, in which 12 stations are regarded as the reference to generate the corresponding corrections and 21 as the users to assess the performance of the multi-GNSS PPP-RTK in both kinematic and static positioning mode. The results show that the root-mean-square (RMS) errors of the ambiguity float solutions can achieve the same accuracy level of the ambiguity fixed solutions after convergence. The combined GNSS cases, on the contrary, reduce the horizontal RMS of GPS alone with 2 cm level to GPS + Galileo/GPS + Galileo + BDS/GPS + Galileo + BDS + GLONASS with 1 cm level. The convergence time benefits from both multi-GNSS and fixing ambiguities, and the performances of the ambiguity fixed solution are comparable to those of the multi-GNSS ambiguity float solutions. For instance, the convergence time of GPS alone ambiguity fixed solutions to achieve 10 cm three-dimensional (3D) positioning accuracy is 39.5 min, while it is 37 min for GPS + Galileo ambiguity float solutions; moreover, with the same criterion, the convergence time of GE ambiguity fixed solutions is 19 min, which is better than GPS + Galileo + BDS + GLONASS ambiguity float solutions with 28.5 min. The experiments indicate that GPS alone occasionally suffers from a wrong fixing problem; however, this problem does not exist in the combined systems. Finally, integer ambiguity resolution is still necessary for multi-GNSS in the case of fast achieving very-high-accuracy positioning, e.g., sub-centimeter level.

Precise point positioning (PPP) is one of the well-known applications of Global Navigation Satellite System (GNSS) and provides precise positioning solutions using accurate satellite orbit and clock products. The tropospheric delay due to the neutral atmosphere for microwave signals is one of the main sources of measurement error in PPP. As one component of this delay, the hydrostatic delay is usually compensated by using an empirical correction model. However, how to eliminate the effects of the wet delay during a weather event is a challenge because current troposphere models are not capable of considering the complex atmosphere around the receiver during situations such as typhoons, storms, heavy rainfall, et cetera. Thus, how positioning results can be improved if the residual wet delays are taken into account needs to be investigated . In this contribution, a real-time procedure of recursive detection, identification and adaptation (DIA) is applied to detect the model errors which have the same effects on both phase and code observables; e.g., the model error caused by the tropospheric delay. Once the model errors are identified, additional parameters are added to the functional model to account for the measurement residuals. This approach is evaluated with Global Positioning System (GPS) data during two rainfall events in Darwin, Australia, proving the usefulness of compensated residual slant wet delay for positioning results. Comparisons with the standard approach show that the precision of the up component is improved significantly during the periods of the weather events; for the two case studies, 72.46% and 64.41% improvements of root mean squared error (RMS) resulted, and the precision of the horizontal component obtained by the proposed approach is also improved more than 30% compared to the standard approach. The results also show that the identified model errors are concentrated at the beginning of both heavy rainfall processes when the front causes significant spatial and temporal gradients of the integrated water vapor above the receiver.

This contribution implements the Kriging interpolation in predicting the tropospheric wet delays using global navigation satellite system networks. The predicted tropospheric delays can be used in strengthening the precise point positioning models and numerical weather prediction models. In order to evaluate the performances of the Kriging interpolation, a sparse network with 8 stations and a dense network with 19 stations from continuously operating reference stations (CORS) of the Netherlands are selected as the reference. In addition, other 15 CORS stations are selected as users, which are divided into three blocks: 5 stations located approximately in the center of the networks, 5 stations on the edge of the networks and 5 stations outside the networks. The zenith tropospheric wet delays are estimated at the network and user stations through the ionosphere-free positioning model; meanwhile, the predicted wet delays at the user stations are generated by the Kriging interpolation in the use of the tropospheric estimations at the network. The root mean square errors (RMSE) are calculated by comparing the predicted wet delays and estimated wet delays at the same user station. The results show that RMSEs of the stations inside the network are at a sub-centimeter level with an average value of 0.74 cm in the sparse network and 0.69 cm in the dense network. The stations on edge and outside the network can also achieve 1-cm level accuracy, which overcomes the limitation that accurate interpolations can only be attained inside the network. This contribution also presents an insignificant improvement of the prediction accuracy from the sparse network to the dense network over 1-year’s data processing and a seasonal effect on the tropospheric wet delay predictions.